A few months ago, I decided to take up photography, so I went out and bought the Nikon D3100 pack that came with the 18-55mm kit lens. A few months after that, I bought the 55-200mm (for reasons I dont know of now). Recently I've been watching videos about lenses and flash photography, so I sold both of my lenses and got the 35mm f/1.8 and an SB-600 and it has the best decision of my photographic career.
As it is, I don't really have the money to buy a lens, but I'm willing to save up maybe $700 to pick up another lens.
I'm mainly interested in doing walk-around street photography, and I wanted to know what lens (from either Nikon or a 3rd party lens maker) would be good for that.

Street photography can be done with any and all lenses. The classification refers more to they kind of images and the style of shooting, than the tech used to create it.

Some believe that Street Photography require the shooter to get up close and personal with the subject matter, to really count. Others focus more on the composition and the subjects.

Common to most schools of thought is the idea that you walk around and observe what happens, then takes the shots very quickly in the hope that you catch something authentic and original. For that reason, many street photographers set their lenses at a hyperfocal length, giving maximum DOF. This allows you to shoot very quickly without having to wait for auto-focus.

The Nikon 35mm F1.8 is a classic street photographer's lens - in fact, I believe Nikon made this to commemorate Henri Cartier-Bresson who is one of the pioneers of street photography.

But there are no rules of course - some use zooms, others use cell-phones, rangefinders, lomo-cameras...whatever works.

But if there is any common thread - lens-wise - in street photography, it's the idea of speed. It's impulsive, intuitive and largely a "shoot from the hip" approach that favor candid shots. And for that, the 35mm is excellent.

I'd like to second what LahLahSr stated. I'd also like to suggest a wide-angle lens. I've been shooting street with my 35mm for some time now but there have been numerous occasions where I wanted to capture the environment around by subject while being close at the same time. Unfortunately, the 35mm just isn't wide enough to do this so I've been looking into a wide-angle lens.

You might consider the 18-105 as providing a WA option (and a good one) and also a lens that lets you adjust focal lengths (within a very useful range) to take advantage of differing situations you might encounter. And it's reasonably priced.